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Quadratic Equations

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsFor the equation \\((q+2)x^2-2(q-1)x+q=0\\), which value of \\(q\\) gives equal roots, given that \\(q\\ne-2\\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIn (q + 2)x² − 2(q − 1)x + q = 0, with q ≠ −2, what is the value of q for equal roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf p ≠ 1 in (p − 1)x² − 2(p + 1)x + (p + 3) = 0, what is the condition on p for real roots?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsFor the quadratic equation \(x^2-(s+4)x+4s=0\), what must be the value of \(s\) for its roots to be equal?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsFor the equation \(x^2-(r+5)x+5r=0\) to have two real and distinct roots, which of the following conditions is correct?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf x² − 2(k − 3)x + (k² − 8k + 20) = 0 has no real roots, what is the correct condition on k?Class 10Quadratic EquationsNature of RootsLevel 38Hard MathematicsIf the roots of the equation \(x^2-2(k+2)x+(k^2+3k+7)=0\) are real, which condition on \(k\) is necessary?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsWhat is the nature of the roots of the equation \\(5x^2-2\\sqrt{30}x+6=0\\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsChoose the correct conclusion about the nature of the roots of the equation \(3x^2-4\sqrt{3}x+5=0\).Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsWhat is the nature of the roots of the quadratic equation \(2x^2-6\sqrt{2}x+9=0\)?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf (a\neq0) and (D=b^2-4ac) is negative in (ax^2+bx+c=0), what is the correct statement about the graph and roots?Class 10Quadratic EquationsNature of RootsLevel 38Expert MathematicsIf the equation \(x^2-2(a-1)x+(a^2+1)=0\) has no real roots, which condition on \(a\) is correct?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf a and b are real numbers, a \(\neq\) b, and \(x^2-(a+b)x+ab=0\), what will be the nature of the roots of this quadratic equation?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf \\(x^2-(2a+1)x+a(a+1)=0\\), where \\(a\\) is a real parameter, what will be the nature of its roots?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsA number puzzle gives the equation \(n^2-2pn+(p^2-5p)=0\). What condition on \(p\) is necessary for the equation to have two real and distinct values of \(n\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsAn area situation gives l² - 2(a + 3)l + (a² + 10) = 0. What is the condition on a for real length values?Class 10Quadratic EquationsNature of RootsLevel 37Hard MathematicsIf the equation of a parabola is \(y=x^2-2kx+(k^2-4)\), how will it intersect the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsHow will the parabola \(y=x^2-2kx+k^2\) intersect the x-axis?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsFor a real constant \(k\), how many points of intersection are there between the parabola \(y=x^2-2kx+k^2+1\) and the \(x\)-axis?Class 10Quadratic EquationsNature of RootsLevel 37Expert MathematicsIf \(r\) is any real number, what is the correct conclusion about the nature of the roots of the equation \(x^2-2rx+(r^2+9)=0\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert